The suggestion casts a question mark over one of the central aims of Chancellor George Osborne's spending review – to cap overall welfare spending from 2015/16 – can be achieved.

Mr Duncan Smith’s department was one of the biggest Whitehall losers in the 2015/16 spending round, seeing its budget fall by 11.6 per cent to £5.2billion. A lot of the changes arcut backs to staffing levels in the department.

The Institute for Fiscal Studies said on Thursday said the DWP had fared the worst for job losses among Whitehall departments. The IFS said that between 2011 and 2016 the department will have lost 40 per cent of is workforce.

A Treasury report containing an analysis from the Office for Budgetary Responsibility which costed the effect of the changes suggested that these cuts could perversely lead to the benefits bill increasing.

A paragraph headlined “DWP operational changes” said: “We have certified the costings included in the Treasury’s policy decisions table for DWP operational measures in isolation.

“However, we note that there have been, and will continue to be, wider operational changes within DWP and across government that are likely to affect the public finances.

“For example, reductions in administrative spending in other areas of DWP could lead to higher net spending on benefits.”

Shadow Work and Pensions secretary Liam Byrne told The Daily Telegraph: "The welfare revolution we were promised has descended into chaos.

"Iain Duncan Smith's department is now such a shambles even his cuts risk pushing up the cost of social security - no wonder the benefits bill is soaring £20 billion higher than planned. David Cameron must get a grip of this fast, before more money is wasted."

Since May 2010 the Public and Commercial Services union said that Work and Pensions has cut 20,000 jobs, most of which have gone in junior administrative staff whose job is to check benefits’ claims.

PCS leader Mark Serwotka said: “Cutting Job Centre staff at a time of high unemployment is the economics of the madhouse because not only does it mean there are fewer people to help find work for the unemployed it simply adds to the dole queues.

“Added to this is the fact that 40 per cent of DWP staff will be eligible for some form of universal credit because of low pay so further pay cuts are also a false economy.”

DWP sources confirmed that the Treasury was concerned that if there were not enough staff to help the unemployed people get back to work, then fewer jobless would get back into the labour market.

In the 2015/16 spending round, unveiled on Wednesday, George Osborne said overall spending on welfare is to be capped from April 2015 to rein in the benefits’ bill.

The Chancellor said on Wednesday the total spent on a range of welfare payments including housing benefit, and tax credits, as well as disability and pensioner benefits will be subject to a limit.

Last year, taxpayers funded £112billion in benefits, which all rose sharply in the decade before the economic crisis.

The detail of the cap will be announced next year and the level at which it is set is expected to be the subject of intense political debate and speculation.

A DWP spokesman said: "This department has a proven track record of getting more people into work while at the same time operating under a tighter budget.

"Further savings will come from being smarter and more efficient about the way we do our day to day work, and we're determined that this will not impact on overall welfare savings - in fact, the Chancellor announced more support to get jobseekers back to work in the Spending Round."